Physics for Scientists and Engineers
6th Edition
ISBN: 9781429281843
Author: Tipler
Publisher: MAC HIGHER
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Chapter 35, Problem 4P
To determine
The value of force constant for entire spring.
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Students have asked these similar questions
Atoms vibrate relative to one another in molecules with the bond acting as a spring.
Consider the H – CI bond, where the heavy Cl atom forms a stationary anchor for the very
light H atom. That is, only the H atom moves, vibrating as a simple harmonic oscillator.
(a) Give the equation that describes the allowed vibrational energy levels of the bond.
(b) The force constant kf for the H – Cl bond is 516.3 N m'1. Given the mass of H equal to
1.7 x 1027 kg, determine the difference in energy (separation) between adjacent energy
levels.
(c) Calculate the zero-point energy of this molecular oscillator.
What is the minimum energy required to go from one vibrational state to the next higher vibrational state for a molecule whose vibrations are modeled by a harmonic oscillator?
The greenhouse-gas carbon dioxide molecule CO2
strongly absorbs infrared radiation when its vibrational
normal modes are excited by light at the normal-mode
frequencies. CO₂ is a linear triatomic molecule, as
shown in (Figure 1), with oxygen atoms of mass mo
bonded to a central carbon atom of mass mc. You
know from chemistry that the atomic masses of carbon
and oxygen are, respectively, 12 and 16. Assume that
the bond is an ideal spring with spring constant k.
There are two normal modes of this system for which
oscillations take place along the axis. (You can ignore
additional bending modes.) In this problem, you will find
the normal modes and then use experimental data to
determine the bond spring constant.
Figure
O
1
mo
1x₁
2
mc
1 of 1
3
mo
1Xz
Part A
Let x₁, x2, and 3 be the atoms' positions measured from their equilibrium positions. First, use Hooke's law to write the net force
on each atom. Pay close attention to signs! For each oxygen, the net force equals mod²x/dt². Carbon has a…
Chapter 35 Solutions
Physics for Scientists and Engineers
Ch. 35 - Prob. 1PCh. 35 - Prob. 2PCh. 35 - Prob. 3PCh. 35 - Prob. 4PCh. 35 - Prob. 5PCh. 35 - Prob. 6PCh. 35 - Prob. 7PCh. 35 - Prob. 8PCh. 35 - Prob. 9PCh. 35 - Prob. 10P
Ch. 35 - Prob. 11PCh. 35 - Prob. 12PCh. 35 - Prob. 13PCh. 35 - Prob. 14PCh. 35 - Prob. 15PCh. 35 - Prob. 16PCh. 35 - Prob. 17PCh. 35 - Prob. 18PCh. 35 - Prob. 19PCh. 35 - Prob. 20PCh. 35 - Prob. 21PCh. 35 - Prob. 22PCh. 35 - Prob. 23PCh. 35 - Prob. 24PCh. 35 - Prob. 25PCh. 35 - Prob. 26PCh. 35 - Prob. 27PCh. 35 - Prob. 28PCh. 35 - Prob. 29PCh. 35 - Prob. 30PCh. 35 - Prob. 31PCh. 35 - Prob. 32PCh. 35 - Prob. 33PCh. 35 - Prob. 34PCh. 35 - Prob. 35PCh. 35 - Prob. 36PCh. 35 - Prob. 37PCh. 35 - Prob. 38P
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- Q.3 a) Which type of molecules exhibit infra-red spectra? Calculate the vibrational energy and force constant of 'H"F if its vibrational frequency is 3.0 x 1014 Hz. b) Prove that the eigenvalues of a Hermitian operator are real.arrow_forwardThe diatomic radical, 160¹H, can be treated approximately as a harmonic oscillator, with a force constant of 780.7 N/m, mH = 1.007825 Dalton, and mo = 15.9949146 Dalton. (a) What is the harmonic angular frequency, w, of this oscillator (in sec¯¹)? (b) Spectroscopic measurements are often used to characterize molecular oscillators, and in doing so, they relate a wavelength of light to its characteristic oscillation frequency through the relation, w = 2πc. Use this to find in units of cm-1 (wavenumbers). λ = (c) If the force constant is the same, what would be in wavenumbers (cm-¹) for ¹60 ²H (²H = deuterium), with mH = 2.014101778 Dalton?arrow_forwardThe force constant of the Cl2 molecule is 323 Nm-1. Calculate the energy at the zero point of vibration and if this amount of energy is converted to translational energy, how fast would the molecule be moving?arrow_forward
- Consider a Face Centered Cubic (FCC) lattice structured Nickel crystal. We are looking to find the surface energy of the new surface that is formed after it is sliced at the (100) plane. a- Find the value of R as function of the lattice constant a. 4R Oa = 2R Oa = 4R Oa = = 2/2R V2 Find the area A11 of (111) surface as function of R. 04R? O16R? O8R? OR? How many atoms lie on the plane (111) within the unit cell? N111 = atoms within the unit cell Find the number of atoms per unit surface area. 2 2 R2 8R2 16R? 4R? Which of the following represents the expression of the surface energt? ON BEPAarrow_forwardWhy do we need to find the derivative then if we only use 6.5 paired with sin and 2.3 paired with cos? When we find the derivative, do they not switch?arrow_forwardA simple harmonic oscillator is in the ground state with A-², where A=1/41/4 jm-1/2 and a = 1/2 m2, What is a (x²) and Ax? (Hint: [ [_xe-x²³ dx=0 and [_x²a-b²³dx==√m/6²³ ) Ax- μm m2 umarrow_forward
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